MAY 1980 JOHN E. WALSH AND ANTHONY MOSTEK 615A Quantitative Analysis of Meteorological Anomaly Patterns Over the United States, 1900-1977 JOHN E. WALSH AND ANTHONY MOSTEKLaboratory for Atmospheric Research, University of Illinois, Urbana 61801(Manuscript received 5 October 1979, in final form 22 January 1980)ABSTRACT Monthly meteorological data for the years 1900-77 are used in an eigenvector analysis of the anomalypatterns of surface temperature, precipitation and sea level pressure over the United States. Approximately 70% of the variance is contained in the first three of 61 temperature eigenvectors and in the firstthree of 25 pressure eigenvectors. Large-scale patterns of precipitation are also identified, although thecompression of the data is somewhat less effective. The first eigenvector of each variable containsanomalies of the same sign over most of the United States; the second and third modes describegradients in approximately perpendicular directions. Cross correlations between the amplitudes of eigenvectors of different variables are statisticallysignificant, consistent with physical expectations, and, in some cases, are seasonally dependent. Thefirst modes of both temperature and pressure are most persistent in the summer. Persistence on theseasonal time scale is generally largest for temperature and largest when summer is the antecedentseason. The seasonal persistences of the amplitudes of the temperature eigenvectors are generally consistent with the persistences of station temperatures obtained recently by Namias (1978). The most prominent feature of the frequency spectra is a strong peak at 2.1 years in the amplitude ofthe third temperature eigenvector.1. Introduction. Meteorological fldctuations on monthly andseasonal time scales have stimulated a variety ofquantitative investigations in recent years. The emphasis on these scales is partially attributable to thefact that the month has been a convenient althoughsomewhat arbitrary time unit in the compilation ofmeteorological data. Perhaps more importantly,meteorological anomalies over monthly and seasonal time scales often have substantial economicimpacts on activities such as agricultural productionand energy usage. The monthly and seasonal scalesare also the longest for which extended-rangeweather outlooks are typically issued by nationalweather services. Since the large body of researchon monthly-to-seasonal meteorological :fluctuationsprecluc~es a thorough literature review, the following sun, mary will be limited to those studies thatare the most recent and/or pertinent to the presentwork. The statistics of the fluctuations of surface (station) temperatures have been analyzed by Landsberg et al. (1963), van Loon and Jenne (1975),Madden and $hea (1978) and Brinkmann (1979).Namias (1952, 1978) has analyzed the persistence ofmonthly meteorological anomalies, with an emphasis on the geographical dependence of the persistence of temperature. In studies suclh as these,0027-0644/80/050615-16508.00c 1980 American Meteorological Societymaps constructed from temperature trends andstatistics for individual stations have been used toillustrate the spatial coherence of temperaturechanges over time scales of months to decades.van Loon and Williams (1976a,b) and Williams andvan Loon (1976) have computed trends of sea levelpressure, which were then related to temperaturechanges in various regions. Brier (1947) has alsocomputed trends in Northern Hemisphere pressure,while Trenberth (1975) and Madden (1976) haveused spectral methods in analyses of sea levelpressure fields. Several studies have examined the spatial modesof meteorological variations, primarily by the use ofempirical orthogonal functions (also referred to aseigenvectors or principal components). Because ofthe spatial coherence of anomaly fields over regions of substantial agricultural production, energyconsumption, etc., pattern analysis can be a valuabletool in the study of meteorological fluctuations.Gilman (1957) used data from 40 winters to formulate eigenvectors of temperature over the UnitedStates and pressure over the Northern Hemisphere.Sellers (1968) constructed eigenvectors of precipitation over the western United States for each monthof the year. Kutzbach (1970) computed eigenvectorsof the January and July fields of sea level pressureover the Northern Hemisphere, while Kidson (1975)constructed eigenvectors of temperature, precipita616 MONTHLY WEATHER REVIEW VOLUME 108TABLE 1. Stations used in construction of temperature and precipitation eigenvectors.Eastport, ME Hatteras, NC Abilene, TXBlue Hill, MA Asheville, NC Galveston, TXAlbany, NY Charleston, SC El Paso, TXOswego, NY Macon, GA Havre, MTMontreal, QUE Jacksonville, FL Helena, MTNew York, NY Pensacola, FL Sheridan, WYWashington, DC Key WeSt, FL Denver, COLynchburg, VA New Orleans, LA Santa Fe, NMPittsburgh, PA Vicksburg, MS Boise, IDCincinnati, OH Little Rock, AR Salt Lake City, UTColumbus, OH St. Louis, MO Winnemucca, NVDetroit, M! Des Moines, IA Phoenix, AZAlpena, MI Bismarck, ND Yuma, AZMarquette, MI Rapid City, SD Spokane, WAMadison, WI Huron, SD Walla-Walla, WADuluth, MN Omaha, NE Portland, ORMinneapolis, MN North Platte, NE Mt. Shasta, CAChicago, IL Topeka, KS Sacramento, CACairo, IL Dodge City, I~S San Francisco, CANashville, TN Amarillo, TX Long Beach, CA San Diego, CAtion and sea level pressure in both hemispheresand in the tropics using 10 years of data. Barnett(1978) analyzed eigenvectors of winter-averaged andannually averaged surface temperature over bothocean and land areas of the Northern Hemispherefo~-the 1950-77 period. Trenberth (1975) and Davis(1978) used empirical orthogonal functions to studyair-sea interactions, while Walsh and Johnson (1979)used a similar approach to study the associationsbetween interannual atmospheric variability andarctic sea ice extent. Barnett and Preisendorfer(1978) analyzed climatic predictability by formulating eigenvectors of several variables in "key regions'' identified by a filtering procedure. Inanother recent application of the eigenvector approach, Steyaert et al. (1978) used eigenvectorsof sea level pressure as predictors of wheat yieldsin North America and the Soviet Union. The present work is an application of the eigenvector approach to an analysis of monthly temperature, precipitation and sea level pressure anomaliesover the continental United States. The goals of thework are 1) the identification of the dominantspatial patterns of surface temperature, precipitationand pressure anomalies over the United States onthe monthly and seasonal time scales; 2) an examination of the interrelationships between anomaly fieldsof different variables; and 3) an evaluation of thetemporal statistics of the eigenvector amplitudes inorder to assess their extended-range predictive potential and the seasonal dependence of any suchpotential. The United States was chosen because itis a region for which monthly anomaly fields areroutinely analyzed (e.g., Monthly Weather Review,28-105) and forecast by the U.S. National WeatherService. In addition, historical data for this regionare available over a relatively regular network ofstations on a monthly basis since the beginning ofthe 20th century. The present work can be distinguished from the studies referenced above by itsemphasis on the temporal statistics of the eigenvector amplitudes. While time series of eigenvectoramplitudes have been presented by Kutzbach(1967), Kidson (1975) and Newell and Weare (1976),the seasonal -dependence of the eigenvector statistics has received little attention in the literature.These statistics can form the basis for an assessmentof the potential contribution of the eigenvectorapproach to the formulation of monthly and seasonalforecasts of temperature, precipitation and pressureanomaly fields over the continental United States.Moreover, there is mounting evidence (e.g.,Namias, 1974; Rogers, 1976; Harnack and Landsberg, 1978; Harnack, 1979) to support the contentionthat sea surface temperature (SST) fields are of somevalue as extended-range predictors of wintertimetemperature anomalies over the United States.Since .the spatial scales of both SST anomalies andthe stationary atmospheric waves are on the order ofa 1000 km or more, it is not unreasonable to expect that the scales of subsequent meteorologicalanomalies over the United States will be comparable. In other words, if external factors such asSST distributions do indeed contribute to the interannual variability of surface Weather over the UnitedStates, they should affect large-scale patternsof temperature, precipitation and pressure. Empirical orthogonal functions of these meteorologicalanomalies may then b.e convenient aids in the assessment of the effects of SST anomalies and otherexternal factors in a more general temporalframework. While the present work makes heavy use of laggedcorrelations of the coefficients representing anomalyfields, the work can be distinguished from Namias'(1964, 1978) analyses of fields of station autocorrelations. Our focus is on the anomaly patt.ernsand on their temporal statistics. The compression ofa set of data fields by the eigenvector representation permits the discussion- of the large-scaleanomaly patterns 'in terms of a few variable coefficients. The statistics of the coefficients computedfrom sets of meteorological anomaly fields over theUnited States have not previously been reported indetail. Comparisons with the results of Namias'(1978) temperature study will be made in Section 4,where we discuss the time scales (e_.g., persistence)of anomaly patterns. We note here, however, thatan evaluation of the patterns of persistence is notequivalent to an evaluation of the persistence ofanomaly patterns.2. Data The data consist of monthly values' of surfacetemperature, precipitation and sea level pressure forMAY 1980 JOHN E. WALSH AND ANTHONY MOSTEK 617the years 1900-77, inclusive. A total of 936 monthlyfields of each variable are therefore included in theanalysis. The temperature and precipitation data arestation values obtained from the World MonthlyStation Climatology, which is stored on magnetictape in the data collection of the National Centerfor Atmospheric Research (NCAR). The temperature and precipitation eigenvectors are based on anetwork of 61 stations (Table 1) for which the 78year records were complete. In the case of an occasional missing value (131 of 57 096 temperatures;152 of 57 096 precipitations), the missing value wasreplaced by the monthly mean for the 30-yearperiod centered on the year of the missing month.While complete data records exist for U.S. stationsother than those used here, stations in closeproximity to the 61 stations of Table 1 were notincluded in order to maintain some degree of spatialhomogeneity in the data network. An overweightingof station-dense regions was therefore avoided in theconstruction of the eigenvect6rs. The monthly pressure values were obtained fromthe set of Northern Hemisphere sea level gridsarchived at NCAR. Although the grid intervals inthis data set are 5- latitude and 5- longitude,alternate longitudes were omitted in order that thenorth-south and east-west grid distances be comparable. A 25-point (5- latitude x 10- longitude) gridtherefore covers an area approximating that of thecontinehtal United States.3. MethodoBogy The focus of this work is on variability over themonthly and seasonal time scales. Long-termtrends, which have been shown to be statisticallysignificant on the decadal to centennial time scales(e.g., van Loon and Williams, 1976a,b; Brinkmann,1979) are therefore removed from all the time seriesby expressing each data value as a departure fromthe monthly mean for the 30-year period centered(within one year) on .the appropriate year. In thecases of data values for the first and final 15 years ofthe study period, the monthly means were based onthe first or final 30 years, i.e., the 30-year meanswere not centered on the year of the corresponding data values during the first and final 15 years.The 30-year averaging period was chosen only because it has traditionally been used to define "normals" in meteorological and climatological applications. We note parenthetically that LeDuc et al.(1973) have argued that 30 years is not the idealchoice for the computation of temperature normals. The data were also normalized in order to preventareas and seasons of maximum variance fromdominating the eigenvectors. In symbolic form, thenormalization is given by f~. - (t~30)im f~n - , (1)where f;n is the normalized value of the observation fin of a meteorological variable (temperature,precipitation or pressure) at the ith station in thenth month of the 936-month series; (/x30)~,~ is the30-year mean value off in the ruth month of theyear (m = 1, 2, . . . , 12) at the ith station, ando-~,~ is the standard deviation of the departure offfrom the 30-year mean during month m at station i.As discussed in Section 4a, Eq. (1) was found toproduce the most effective compression of the precipitation data into eigenvectors despite the fact thatthe slightly skewed distribution of monthly precipitation totals does not transform under (1) to aperfectly normal distribution. It should also be notedthat the subtraction in (1) of the 30-year mean for theappropriate calendar month removes the seasonalcycle as well as the long-term trends. The fields of fin were then represented in termsof empirical orthogonal functions (eigenvectors).Kutzbach (1967) and Sellers (1968) outline theformulation of empirical orthogonal functions, whileStidd (1967) presents a relatively nonmathematicaldiscussion of the construction and interpretation ofeigenvectors. Briefly, the functions and their associated eigenvalues are the solutions of an eigenvector equation formulated in terms of the samplecovariance matrix (61 x 61 or 25 x 25 in this study).The first eigenvector is the dominant mode of variability of the sample of data fields in the sense thatit represents a maximization of the explained variance. Each succeeding eigenvector describes amaximum of the variance that is unexplained bythe previous eigenvectors. The coefficient or amplitude of an eigenvector is a measure of the extentto which that eigenvector pattern is present in aparticular anomaly field. The various time series ofeigenvector coefficients can then form the basis of astatistical analysis such as the one presented here.Because the first eigenvectors account for a greaterportion of the variance of a set of data fields thanany other combination of the same number of parameters or functions, empirical orthogonal functionsgenerally permit an effective compression of thedata. Other useful properties of the functions aretheir orthogonality, which ensures statistical independence in predictive applications, and the factthat the eigenvalue of a particular eigenvector isa convenient quantitative measure of the variancedescribed by that eigenvector.4. Resultsa. Spatial anomaly patterns The first three eigenvectors of temperature (T),precipitation (R).and sea level pressure (S) areshown in Figs. 1,2 and 3, respectively. These eigenvectors are computed from the normalized departures from 30-year (running) monthly means as described in Section 3. The data for all 936 months618 MONTHLY WEATHER REVIEW VOLUME108 '0 0.10 ~ 10 T1 : 38.0%tures over most of the country. The largest departures are in the Ohio Valley. T, describes 38%of the total temperature variance. T2, on the otherhand, represents a relatively strong east-westgradient in the temperature anomaly field. Theanomaly centers of T2 are in the northern RockyMountain states and in the extreme southeasternpart of the United States. Positive values of thecoefficient of T~ will correspond to slightly abovenormal temperatures east of the Mississippi Riverand to considerably below-normal temperatures inthe western states. The third temperature eigen FiG. 1. The fi~'st three eigenvectors of surface temperatureconstructed from all 936 months (1900-77) of data. Percentagesof variances described by the eigenvectors are shown belowand to right of each map. W (rearm) and C (cool) indicateanomaly centers.were used to construct the eigenvectors in Figs.1-3. The fractions of the total Variance describedby the eigenvectors are indicated in the figures.The total numbers of eigenvectors are'61 each oftemperature and precipitation, and 25 of pressure. The broad scales of ,the anomaly patterns areapparent in the figures'. T~ contains positiveanomalies over all but the far western UnitedStates. Positive values of the coefficient of T~will therefore correspond to above-normal tempera -0.20 ' ~~! -0.10 -0.20 iiiiii ::::::::::::::::::::::::::::::::-0.~0 i:~iiii!!i!iiiiiiiiiiiiiii 0.10 -0.10. R~ : 6.7% .~ FIG. 2. The first three eigenvectors of precipitation constructedfrom,all .936 months (1900-77) of data. Percentages of variancedescribed by the eigenvectors are shown below and to right ofeach map. H (high) and L (low) indicate anomaly centers. _ .,,,..._~. - O. 2 . - O. 10 ~ ~ - :i!!i!i!iiiiiiiiiii d[:i:i:i ........ ~ - O. 10 ~ iii~ ...... . .................. iii - ??:?~::iiiii?~ ..... - :::::::::::::::::::::::: i~ ::ii:: ::::::::::::::::::::::::::::: ...... ' ?~ , _0,~0* .~10~20 ~ ~ .10d' . ............. , -0.10 ,--.- r3 : 10.0gMA-1980 JOHN E. WALSH AND ANTHONY MOSTEK 619 vector Ta represents a north-south gradient in the anomaly field. Positive values of the coefficient of Ta will correspond to above-normal temperatures in the northern states and below-normal temperatures in the South. We note here that the patterns in Fig. 1 are quite similar to the wintertime tempera ture eigenvectors computed by Gilman (1957), al though Gilman's second temperature eigenvector described over 30% of the (wintertime) var/ance. R~, the first eigenvector of the normalized de parture from the monthly mean precipitation, is shown in Fig. 2a. As in the case of T~, the anomaly is of the same sign over nearly the entire United States; only southern Florida and the Rio Grande Valley contain departures of the opposite sign. The position of the anomaly center in the Ohio Valley is also close to that of Tt. Re represents an east-west gradient in the precipitation anomaly field; the departures in the eastern and Gulf coast states are opposite in sign to those over the rest of the country. Ra contains departures of the same sign in the Northwest and in the Northeast, together with departures of the opposite sign in the southern and central states. Fig. 3 shows the first three eigenvectors of the normalized departures of sea level pressure. S~ con tains anomalies of the same sign at every grid point,- thereby representing a general excess or deficit of mass. The largest anomalies are found in the central United States. The second and third pressure eigenvectors (S2 and Sa) correspond to generally east-west and north-south pressure gradients, re spectively. The geostrophic implications of these anomaly gradients will be noted when the tempera ture-pressure and precipitation-pressure relation ships are discussed in Section 4c. The three eigenvectors of Fig. 3 are quite different from the U.S. portions of Kidson's (1975, Fig. 3) hemispheric pressure eigenvectors, presumably because most of the hemispheric variability occurs in areas other than the United States. The fact that the data in Kidson's study were not normalized by the local standard deviations may also contribute to the differences between the two sets of eigenvectors. The cumulative fractions of variance, described by the three sets of eigenvectors are shown in Fig. 4. The rapid convergence of the temperature and pressure curves is apparent: the first four (of61) temperature eigenvectors describe over 75% of the temperature variance, while the first four (of 25) pressure eigenvectors describe over 80% of the pres sure variance. The effectiveness of the data com pression resulting from the eigenvector formula tion is evident. The convergence of the precipita tion curve is considerably less rapid, as 10 (of 61) eigenvectors are required to describe 50% of the precipitation variance. The slower convergence is indicative of the relatively large scatter that is-0.15 \ -0.1551 : 44.4g -0.10 O_ 0 10 0.20 .- O. 2 :~iii!~iii~ 0 ~ .20 - ...... "~'~':~:~:~ ~x~~ O. 10 -0.10 0 S2 : 17.6% 0.10 0.30 0~. 0.20\ = a, -0.10 .:.:.::i~..-0.20 - "'~~i:iiiiiiiiiiiii~~~~ - "::::~:!i:.~/ 0 30 0.10 0 -0.10 't 0.20 ! .t ..~-0.20 ,-- i'.~V - '":-- "~l"'::::'T!i! 1 -0.20 S3 : 11.6% FIG. 3. The first three eigenvectors of sea level pressure constructed from all 936 months (1900-77) of data. Percentages ofvariance described by the eigenvectors are shown below and toright of each map. H (high) and L (low) indicate anomalycenters.typically encountered in precipitation data. Namias(1968, Fig. 1.3) shows a very similar relationshipbetween the cumulative variances explained b~ temperature and precipitation eigenvectors derivedfrom U.S. station data. Despite the slower convergence of the precipitation curve, the eigenvector formulation still permits considerable improvement over the linear variance increase thatwould result from a direct use of the (normalized)station data; the latter situation is shown as adashed line in Fig. 4. We interpret the precipita629MONTHLY WEATHER REVIEWVOLUME 108 1.0 0.9 0 ' I 0 10 20 30 40 50 60 ,VM~E~ 0F [~0~aVECX0RS FIG. 4. Cumulative fractions of variance descNbed by the eiBenvectors of surfacetemperature (T), precipitation (R) and sea level pressure (S). Dashed line represents linear increase of variance.tion patterns of Fig. 2 as the most efficientrepresentations of broad-scale precipitation anomalyfields containing considerable amounts of smallscale noise. While alternative representations of thedata fields (e.g., averaging over various regions)would smooth much of the small-scale noise, wecontend that the large-scale patterns would besimilar to those of Fig. 2. Spatial averaging would,however, obscure the signal/noise information thatis implicit in the eigenvalue-derived variancefractions. The construction of the eigenvectors of Figs.1-3 involves several apparently arbitrary choices,one of which is the normalization of the monthlydata. (Since the effect 'of the data normalizationis dependent on the geographical variability oftrim and hence on the spatial domain, the following.results cannot be extrapolated to studies of otherregions.) Fig. 5 shows the first eigenvector ofeach variable based on non-normalized data, i.e.,values derived from (1) without the division byO'lm. The normalization has little effect on thetemperature and pressure eigenvectors, although the"normalized" anomaly centers are displaced several hundred 'kilometers from the corresponding"non-normalized" anomaly centers. The northwestward displacement of the center of T~ in the nonnormalized case is toward the region of the largeststandard deviation of. the monthly temperatureanomalies. The higher eigenvectors of non-normalized temperature and pressure show similarresemblances to the corresponding normalizedeigenvectors. In the case of precipitation, however, the normalization has a considerable effect on the computedeigenvectors. The "non-normalized" vector Ricontains large components in the southeasternUnited States and especially along the Gulf coast.The secofid non-normalized eigenvector (R~, notshown) also contains intense anomaly pockets inhigh-rainfall areas (e.g., northern California, theFlorida peninsula). Since the areas of heavy rainfall are generally those with the largest standarddeviations about the monthly mean precipitation,the variance within an. individual eigenvector isdistributed considerably more evenly when the dataare normalized prior to the eigenvector construction. However, large-scale precipitation fluctuationsin areas of marginal precipitation (e.g., the midwestern and Great Plains states) often affectlarger portions of the population and have greatereconomic implications than do fluctuations in thewettest areas of the country. We therefore choseto work with "normalized" precipitation data transformed 'according to (1). Moreover, considerableexperimentation with alternative (e.g., logarithmic)representations of the skewed distribution ofmonthly precipitation values failed to produce aset of eigenvectors that compress the data moreeffectively than do the patterns of Fig. '2. Another strategy in the eigenvector formulation isa monthly stratification of the data prior to theeigenvector computations. Specifically, we mayconstruct 12 gets of eigenvectors based on 78months each (78 Januarys, 78 Februarys, etc.)rather than a single set based on all 936 months.The monthly stratification presumarly allows for thepossibility that the dominant modes of variabilityare seasonally dependent. Figs. 6 and 7 contain thefirst temperature and precipitation eigenvectorsbased on the two climatologically extreme months-January and July. The first temperature eigenvectorMAY 1980 JOHN E. WALSH AND ANTHONY MOSTEK 621(Fig. 6) changes surprisingly little from Januaryto July, although the fraction of variance described by the first eigenvector is smaller in summer than in winter (33.1% vs 41.8%). Whilechanges in R~ (Fig. 7) are apparent in the southeastern and southwestern corners of the UnitedStates when the data are restricted to a singlemonth, the dominant feature (an anomaly centeredover the midwestern states) appears consistentlythroughout the year. The variance fractions described by the first precipitation eigenvector (19.5%in January, 9.3% in July) are indicative of thetendency for summer precipitation to be: more scattered than-winter precipitation. The sea levelpressure eigenvectors (not shown) computed for individual months contain less month-to-month variability than either the temperature or precipitation eigenvectors. Interestingly, it was found thatthe cross-correlations and autocorrelations betweenthe coefficients of different eigenvectors were nolarger when the eigenvectors were based on themonthly stratified data rather than on the unstratifieddata. The results in the following subsections aretherefore based on the eigenvectors derived fromthe single 936-month (unstratified) set of anomalyfields. Finally, we note that computed eigenvectors canbe affected by the shape and scale of the datanetwork (Buell, 1979). In some cases this effectmay dominate seasonal variations in the first feweigenvectors. It is therefore possible that the similarity of the seasonally extreme patterns of Figs. 6and 7 is at least partially attributable to boundaryeffects.b. Representation of extreme months and seasons The extent to which the eigenvectors can represent individudl anomaly fields is illustrated in Fig. 8,which shows the observed departures from the normal temperature fields for the three months inwhich the coefficients T~, T: and Ta attained theirmaximum values. The resemblance of September1918 (T~ = -14.2), January 1937 (T2 = +14.7) andDecember 1933 (Ta = -8.4) to the respective eigenvectors is quite strong. Similar agreement with observed anomaly fields was found in those monthswhen the precipitation and pressure coefficientsreached extreme values. While the "severity" ofweather over a monthly or seasonal period cannotbe equated with the magnitude of a particulareigenvector, we may expect that regional anomalieswill generally coincide with the occurrence of extreme values of the coefficients of the dominanteigenvectors. Accordingly, we have listed in Table 2the five years corresponding to the largest positiveand negative values of the 3-month means of thecoefficients of the first temperature and precipitao _- -' ~-~~2_~~~- o.lo~ o i0.10 R~ : 12.9% 0.20 ~0.20I h \l ~ ~ ~ I ~ 0.15 0.10 Si : 46.0% FIG. 5. The first eigenvectors of surface temperature (T0,precipitation (R0 and sea level pressure (S0 based on nonnormalized departures from monthly means.tion eigenvectors. Two periods which contributenoticeably to the list of extreme seasons are the1930-39 decade and the final two years (1976-77)of the study period. The three most extreme valuesof T~ and five of the eight positive (dry) extremes of R~ occurred during the 1930's. The mostnegative (cold) autumn value of Tt occurred in1976, the most positive (dry) winter value of R~ in1977, and the most positive (warm) spring value ofT~ in 1977. In addition, the recently computedcoefficients of T~ for the winters of 1978 (Tt = -8.32)and 1979 (T~ = -6.68) are the second and fourthmost negative winter values of the century.622 MONTHLY WEATHER REVIEW VOLUME 1080.10 ~,~ "~ (T1)JAN : 41.8%-0.10 -0.10 -0.10 (T1)JUL : 33.1% Flo. 6. The first eigenvectors of January and July surfacetemperature based on normalized departures from the monthlymeans. The extreme seasons in Table 2 are generallyconsistent with the results of several recent investigations based on U.S. station data. Specifically,each of the years 1936, 1918, 1963,, 1905 and 1977stands out as a negative peak in one or more ofthe December-February regional temperature plotsof Diaz and Quayle (I978, Fig. 5). The winters of1932 and 1950 are hlso identified by Diaz andQuayle as extremely warm winters in several regionsof the United States. The relatively large number ofextreme .values of R, and Tx during the 1930's isconsistent with Chico and Sellers' (1979) finding thatinterannual temperature variability in the UnitedStates peaked during the decade centered on 1930.While the extremes of the past few years alsoproduced a preliminary increase in Chico andSellers' temporal trend of interannual variability,additional years of data are required before thedecade centered on 1980 can be included appropriately in Chico and Sellers' Fig. 2.c. Cross-correlations at zero lag Fig. 9 shows monthly cross-correlations betweenconcurrent values of the coefficients of the eigenvectors of different meteorological variables. Theplots may be interpreted as annual cycles of correlations between anomaly fields. In order to placethese cross-correlations (as well as the autocorrelations of Figs. 10 and 11) in proper perspective,we note here that the 95 and 99% confidencelimits for a sample size of 78 (years) are 0.22 and0.29, respectively. As might have been anticipatedphysically, the anomaly fields of the different variables are not independent. The negative values of(T~Sa), for example, imply that below-normaltemperatures (negative T0 over the eastern andcentral United States are associated with strongerthan-normal northerly and northeasterly airflow.The negative <T2Ri) imply that positive west-toeast temperature gradients (i.e., temperatures below-normal in the West, above-normal in the East)are associated with above-normal precipitation overmuch of the eastern United States. The enhancedbaroclinicity represented by a positive T2 is consistent with the precipitation increase. An alternative approach to the study of interrelationships between fields of different variablesis Kutzbach's (1967) use of eigenvectors as combined representations of several variables. Kutzbach's data covered all of North America (ex ..... !:ii:~ii::::::::::: :?~: ~i::i~:'- :::::::::::::::::::::o .... ~i:i~i (R].)jUL : 9.3%F~G. 7. The first eigenvectors of January and July precipitationbased on normalized departures from the monthly means.M^- 1980 JOHN E. WALSH AND ANTHONY MOSTEK 623cluding Mexico) but were limited to 25 Januaryfields of surface temperature, pressure and precipitation. A good correspondence can be seen between R~ of Fig. 2 and the precipitation component of Kutzbach's first combined eigenvector,e~; between T1 and T2 of Fig. 1 and the temperaturecomponents of Kutzbach's e2 and ea, respectively;and between P~, P2 and P3 of Fig. 3 and the pressure components of Kutzbach's e~, el and e3, respectively. The synoptic consistency of our cross correlations is also apparent in Kutzbach's combined TABLE 2. Largest seasonal amplitudes of T~ and R,. Seasons aredefined as winter (December-February), spring (March-May),summer (June-August) and autumn (September-November). +3- o iiii~ -3- e,~ o _6o -6- +3-'-~ l[ I::+6- ,,'~'t~k__~|X~[~~::~] ,i ..... R; >0 1977 (4.6)+6o:~_~_~/~~l'~.~ .::.:~ :. .:~ (dry) 1931 (4.3) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ':~~ R~ < 0 1949(-4.1) (wet) 1950 (-4.1) ~3o 1937 (-3.3) +30 ~ 1932 (-2.8) Sept. 1918 1974 (-2.6) 11 = -14.2 ~?~ -~6o-~2- 0 o +8o .o ::::::::::::::::::::::::: '":i ......... ": ~::JJ +8- .... :?: .~ :~::.~-+t2~ ....... "~~~~~~~:~ :7 h [~x, ,~, - ~ +/&'~':?:l/':~: ~ Oan. 1937 ' ~ ' +~T2 : +14,7 0~ _~o -8t ~ ~ ~ ~ o ............ ~' _4~ 6 ~ / ) "~ k +4- - +V ~t ~3~ +~ ~Dec. 1933~ +~ / v T3 = -8.4 F~o. 8. Observed anomaly fields of surface temperature (-F) forSeptember 1918 (from Mon. Wea. Rev., 46, Plate 79), January1937 (from Mon. Wea. Rev., 65, Plate 3) and December 1933(from Mon. Wea. Rev., 61, Plate 134).Winter Spring Summer AutumnT~ > 0 1932 (9.0) 1977 (7.2) 1901 (6.2) 1931 (10.1)(warm) 1954 (5.0) . 1955 (6.2) 1952 (6.0) 1963 (5,2) 1950 (4.8) 1921 (5.7) 1936 (5.3) 1900 (4,8) 1909 (4.5) 1946 (4.4) 1934 (5.3) 1971 (4.6) 1921 (4.3) 1938 (3.9) 1954 (4.9) 1927 (4.3)T~ < 0 1936 (-9.3) 1907 (-5.7) 1927 (-7.4) 1976 (-8.3) (cold) 1918 (-8.3) 1924 (-5,6) 1915 (-7.5) 1917 (-6.7) 1963 (-6.7) 1926 (-5.0) 1967 (-6.2) 1967 (-5.1) 1905 (-6.2) 1940 (-4,8) 1950 (-5.9) 1942 (-4.7) 1977 (-5.1) 1917 (-4.7) 1945 (-5.1) 1951 (-4.2)1934 (3.7) 1930 (3.6) 1939 (3.9)1925 (3.6) 1936 (2.6) 1904 (3.5)1910 (3.3) 1913 (2.5) 1917 (3.3)1940 (3.0) 1910 (2.3) 1953 (3.2)1971 (2.7) 1924 (1.9) 1952 (3.0)1973 (-4.8) 1928 (-4.7) 1919 (-3.7)1945 (-3.7) 1915 (-3.3) 1926 (-3.3)1912 (-3.0) 1975 (-2.4) 1972 (-3.0)1927 (-2.9) 1958 (-2.4) 1911 (-2.9)1929 (-2.9) 1923 (-2.1) 1927 (-2.9)representations, whi'ch imply associations betweentemperature anomalies and geostrophic advectionand between precipitation anomalies and enhancedbaroclinicity.. While Kutzbach's associations are based onJanuary data only, several cross correlations inFig. 9 contain a seasonal cycle that can also beinterpreted physically. The annual cycle of (T~R~),for example, is indicative of the tendency for dryness in the eastern and midwestern United Statesto be associated with below-normal temperatures inwinter and above-normal temperatures in summer.The dry Canadian air masses that generallydominate cold winters in the East and Midwestcontribute to the negative (T~R~) in the wintermonths. During the summer, on the other hand, theincreased surface insolation associated with belownormal precipitation evidently results in warmertemperatures at the surface. Similarly, the negative(T~S~) of winter imply an association betweenwarm temperatures over the South and northwardairflow from the Gulf of Mexico; warm advectionof this type would not be expected during themonths of June-August, when the land-seatemperature gradient is smaller and generally opposite in. sign to that of winter. We also mention here that the magnitudes of thecross-correlations described above generally decrease rapidly with lag. For example, the magnitudesof 91 monthly cross-correlations exceed 0.3 at lag 0.The corresponding totals for lags of 1,2 and 3 monthsare 29, 18 and 11.624 ' MONTHLY WEATHER REVIEW VOLUME 108 0.5 0.4 0,3 0.2 0.1 0-0.1-0.2-0.3 -0.4 < 01-0.1~-0.2-0.3-0.4,-0.5-0.6-0.7-0.8 . 0.?~ 0.6- 0..5~ 0.4 0.3 0.2~0.1 0-0.1 ~-0.2 --0.3 --0.4-0.5 -<T2R:><T~S2>J F MA MJJ ASO N DMONTH<T~R~> l5<T~S~><T3S2>J FM AM JJ AS ON D MONTH' Flo. 9. Cross correlations between the coefficients of the dominant eigenvectorsof surface temperature (T), precipitation (R) and sea level pressure (S). Crosscorrelations are shown for each month of the year (i.e., each bar represents acorrelation between 78 pairs of coefficients). Months are identified by J = January,F = February ..... D = December.d. Persistence of the anomaly fields The month-to-month persistence of the anomalyfields is illustrated in Fig. 10, which shows themonthly values of the lag 1 autocorrelations Of thecoefficients of the first three eigenvectors of eachvariable. Also shown on a monthly basis are "composite'' persistences defined as the weighted sumsof the persistence values of the first three eigenvectors of each variable; the weighting factorsare the fractions of the 3-eigenvector variancedescribed by the individual eigenvectors. The composite persistences are generally largest for temperature and smallest for precipitation. The compositetemperature persistence varies systematicallythrough the year: the persistence is strongestduring summer and Winter, and weakest during_the spring and autumn transition seasons. Theportions of Fig. 10 corresponding to the individualtemperature components indicate that the relativelyhigh summer composite persistences are attributableto the tendency of Tx to persist most strongly duringthe summer (<T1T~)MA---,juN = 0.28,= 0.33, <T~Tx)ju~-,AUO: 0.36). The winter peak inthe composite temperature persistence, on the otherhand, occurs during months when the persistenceMAY 1980 JOHN E. WALSH AND ANTHONY MOSTEK 625 o.4I 0.30.2 0.1-0.( 0.3'- 0.2 0.1 0-0.1 - 0.5h 0.4~ 0.3- 0.1/-0.1 ~ 0.4' 0.3i 0.2 0.1Illl fllllllll <T~T~><T2T2><T~T3> <RzR~>11 <R2R2><R~R~> <RcRc>IIIIIIIIIIII1d FM AM Jd AS ON DMONTH <TcTc> <ScSc>J FM AM JJ AS ON D J FM AM dj AS ON 0MONTH MONTH FIG. 10. Monthly persistence (lag 1 autocorrelation) of the coefficients of thedominant eigenvectors. Also shown, is composite (C) monthly persistence (defined in text) of each variable. Persistences are plotted as functions of the monthsfrom which the anomalies persist.values of T2 and Ta are higher than their annuallyaveraged values. The double peak of the compositetemperature plot is consistent with Narnias' (1952)analysis. The smallness of the persistence duringthe spring and autumn seasons is attributed byNamias to the rapidly changing surface temperatures and land/sea temperature gradients thatcharacterize these seasons. A similar annual regimeis found in the composite persistence of the sea levelpressure anomaly fields: the lag 1 autocorrelationsare larger in summer and winter than in spring andautumn. The similarity between the annual cycles ofthe mode-weighted persistences of temperature andpressure is due at least partially to the dependenceof the temperature anomalies on geostrophic advection. The precipitation modes, however, showessentially no tendency to persist during any season. This lack of persistence was also foundwhen the precipitation eigenvectors were based onnon-normalized data and when the precipitationeigenvectors were computed separately for eachof the 12 months. Persistence on the seasonal time scale is illus*trated in Fig. 11, which shows the autocorrelations of the seasonally averaged coefficients at a lagof one season for cases in which each season isantecedent. The seasons are defined as winter (December-February), spring (March-May), summer(June-August) and autumn (September-November). The persistences are generally positive, although the magnitudes are too small to be of muchvalue in seasonal forecasting applications. When alllags of one to four seasons are considered, themagnitudes of the following persistences exceed 0.3in magnitude: T2 (spring to summer, 0.301; summerto following summer, 0.334), Ta (winter to spring,0.375; autumn to spring, 0.318; winter to followingwinter, -0.327), R~ (summer to autumn, -0.326) andS2 (autumn to summer, 0.303). The seasonal persistence data are synthesized in Table 3, which liststhe composite persistences (defined earlier) for eachvariable by lag and by antecedent season. Thetemperature persistences in Table 3 are accompanied by the corresponding (median) values obtained by Namias (1978) in his analysis of temperature autocorrelations computed for individual U.S.stations from 40 years (1934-73) of data. The temperature portion of Table 3 contains further comparisons with Namias' results in the bottom row andfinal column which list, respectively, the mean autocorrelations for each lag regardless of season andthe mean autocorrelations for each antecedent sea626 MONTHLY WEATHER REVIEW VOLUME 108 0.3 -- <T~I~> 0'2--k~ 0.1 0-0.1-0.2 ~I F <T2T~> 0.3 -- __ 0.~ ~0. I -- I-0.1i 0.4 <T,r3~ 0.3 0.2 o. L._-I-0.1~0.20.--'~F I I I I I W Sp Su ^ SEASON<SiS~><R2R2><S~S2> <RcRc> <ScSc> k_/W Sp Su A W Sp Su A SEASON SEASON FIG. 11. Seasonal persistence of the coefficients of the domi- -nant eigenvectors. Also shown is "composite" (C) seasonal persistence (defined in text) 'of each variable. Persistences areplotted as functions of the seasons from which the anomaliespersist. Seasons are identified by W = winter, Sp = spring, Su= summer, A: autumn.son regardless of lag. The results of the twostudies are quite consistent,' especially when weconsider the differences in the study periods andin the station networks. Some differences arefound, however; between the two sets of temperature values and especially among the three variables(temperature, precipitation and pressure) of thepresent study. The temperature persistences decaymonotonically with lag from 0.15 at a lag of 1 seasonto 0.00 at a lag of 4 seasons. The decay is moreregular than implied by Namias' median autocorrelations, possibly because of the longer studyperiod used' here. Despite the 0.00 autocorrelationof temperature at lag 4, the lag 4 autocorrelations are relatively large in the cases of individualcoefficients for some antecedent seasons: 'T2 (summer to summer, 0.334), Ta (winter to winter,-0.327). The corresponding 95 and 99% confidencelevels are 0.22 and 0.29. The negative value of<T3T~) between successive winters, indicating achange of phase from one winter to the next, isconsistent with the spectral results described in thefollowing subsection. One implication of these values is that small median'or composite autocorrelations for a particular lag do not preclude theexistence of significant autocorrelations of individual spatial patterns at that lag. The lag 4temperature autocorrelations of Table 3 are quiteconsistent with the results of Madden's (1977)analysis of North American station temperatures.-Although his autocorrelations were restricted tosummer and winter temperatures and to lags offour seasons, Madden found that the year-to-yearautocorrelations of station temperatures were generally higher in summer than in winter. Finally,we note that the precipitation and pressure autocorrelations of Table 3 show no tendency to decaywith lag, primarily b~cause the mean autocorrelations are already very'small (0.04 and 0.09) at lag 1. Table 3 shows that the largest autocorrelations (averaged over all lags) of temperature and pressure are found when summer is the antecedent season. This finding agrees with Namias' tabulation of the temperature autocorrelations as a function of antecedent season. However, Table 3 also shows that such general statements can obscure some of the more specific results: the largest of all the composite lagged autocorrelations is the lag 1 tem perature correlation between autumn and winter (<TcTc)~-,w = 0.26). Fig. 11 shows that the three component correlations ar~ in the 0.18-0.30 range in this case. However, the lag 2, 3 and 4 correlations based on autumn as the antecedent season are generally negative, so the largest value in the final temperature column of Table 3 is not the autumn but the summer value. The lag-averaged su, mmer pressure value is also larger than the pressure values for other seasons. The precipitation values in Table 3 are generally very small; the largest are the lag 3 and 4'values (0.13 and 0,14) when summer is the antecedent season. While the results described above have the ad vantage~ that ttiey describe the persistence of large scale patterns rather than of individual station values, their disadvantage is that they fail to dis tinguish regions of high persistence from regions of low persistence. The trade-off between the ap proach used here and the use of station data (e.g., van Loon and Williams, 1976a,b; Namias, 1978) is therefore apparent. Indeed, the Namias study showed that seasonal autocorrelations of tempera ture are generally higher along the west and east coasts than in the central part of the United States.e. Frequency spectra of the eigenvector coefficients Figs. 12, 13 and 14 show the frequency spectra ofthe coefficients of the eigenvectors of Figs. 1, 2 and3, respectively. The associated 95% confidencelimit, based on the appropriate null continuum andcomputed following Mitchell et al. (1966), is shownwith each spectral plot. The spectral computationsMAY 1980 JOHN E. WALSH AND ANTHONY MOSTEKTAnLE 3. Composite seasonal persistences (defined in text) by lag and by antecedent season. Namias' (1978) median temperature correlations are in parentheses.627Antecedent Meanseason Lag 1 Lag 2 Lag 3 Lag 4 (all lags) TemperatureWinter 0.03 (-0.03) O. 17 (0.11) -0.01 (-0.03) 0.03 (0.08) 0.06 (0.04)Spring 0.21 (0.21) 0.08 (0.16) 0.02 (0.05) -0~16 (-0.08) 0.04 (0.18)Summer 0.10 (0.13) 0.16 (0.15) 0:07 (0.06) 0.19 (0.15) 0.13 (0.14)Autumn 0.26 (0.10) -0.03 (0.03) -0.03 (0.03) -0.06 (0.05) 0.04 (0.04) Mean* 0.15 (0.11) 0.09 (0.12) 0.01 (0.01) 0.00 (0.05) PrecipitationWinter 0.03 0.08 -0.04 -0.02 0.01Spring 0.08 0.06 0.04 -0.10 0.02Summer -0.05 0.05 0.13 0.14 0.07Autumn 0.09 0.05 0.10 0.05 0.07 Mean* 0.04 0.06 0.06 0.02 PressureWinter 0.11 0.08 0.00 0.02 0.05Spring 0.15 0.10 0.03 0.08 0.09Summer 0.09 0.10 0.15 0.13 0.12Autumn -0.01 0.10 0.16 0.10 0.09 Mean* 0.09 0.09 0.08 0.08* All seasons.are based on seasonal means of the coefficients,where the seasons are those defined in Section 4d.The raw data are therefore the 312 seasonally averaged values of each coefficient. The first and final30 values of each series were subjected to a cosinetaper (Bendat and Piersol, 1971, p. 323); 48 lags wereused to compute each spectrum. CotTespondingplots (not shown) based on the 936 monthly valuesof each coefficient were very similar 'to the seasonally derived plots, although the former containedmore low-frequency (persistence) energy in the caseof temperature. For a given number of lags, however, the seasonally derived spectra will delineatethe longer (annual to decadal) time scales moreclearly. Also, we note here that 5% of the spectralestimates can be expected to exceed by chance the95% confidence levels. For this reason, the following discussion of Figs. 12-14 does not includespeculative interpretations of the marginally significant peaks. Fig. 12 shows marginally significant peaks at11.9, 0.60 and 0.55 years in. the spectrum of T~; at3.4 years in the spectrum of T2; and at 9.0 and 0.55years in the spectrum of T3. A strong peak,significant at the 99.9% confidence level, is found at2.1 years .in the Ta spectrum. This result suggeststhat the well-known quasi-biennial oscillation (e.g.,Brier, 1978) may manifest itself in the north-southgradient of the temperature anomaly field over theUnited States. Temperature spectra for NorthAmerican stations have also been computed byMadden (1977). While Madden noted spectral peaksnear the quasi-biennial period; his spectra werebased on 64 seasonal means for a single season(summer or winter) at each station. The proximityof the folding frequency to the quasi-biennialperiod therefore precluded a rigorous interpretation of Madden's quasi-biennial peaks. Since the lag 1 autocorrelations of the precipitation coefficients were not significant at the 95% level(Mitchell et al., 1966, p. 60), the peaks in theprecipitation spectra (Fig. 13) were tested for significance against the white noise continuum. Thespectrum of R~ contains several peaks that aremarginally significant at the 95% confidence level.In addition, the peaks in the R~ spectrum at 0.90years and in the Ra spectrum at 2.7 and 0.55 yearsexceed the 95% confidence limits. Peaks in the pressure spectra include those ofSx at 0.80 years and of S2 at 0.89 and 0.52 years.The latter peak, which is significant at the 99% level,corresponds to alternations of northerly andsoutherly airflo~v over the central United States atintervals of approximately 6 months. Finally thepeak at 4.0 years in the Sa spectrum is significantat the 99% level ~/nd is the strongest of all thepeaks in the pressure spectra. While the time scaleof this peak is compatible with that of the Southern628 MONTHLY WEATHER. REVIEW VOLUME 1080.60.40.20.60.40.2 00.80.60.40.20~ [~o 10 4 2 1.5 1.0 0,75 0.50 PERIOD, years Flo. 12. Frequency spectra of the coefficients of the first threeeigenvectors of surface temperature. Detailed lines are 95% confidence levels.Oscillation (e.g., Julian and Chervin, 1978), a crossspectral analysis would be required to establish anassociation.5. Summary -This study has been an analysis of the monthlyanomaly fields of surface temperature, precipitation and sea-level pressure over the continentalUnited States. The primary objective was an evaluation of the temporal behavior of large-scale weatheranomaly patterns. Empirical orthogonal functions(eigenvectors) have. been used to synthesize the936 monthly data fields of each variable. Theresults of the analysis .include the following: I) A very effective compression of the temperature and pressure data is achieved by the eigenvector representation. More than 69% of the temperature variance is described by the first three of61 eigenvectors; more than 73% of the pressurevariance is described by the first three of 25 eigenvectors. The compression of the precipitation datais somewhat less effective: 10' of 61 eigenvectorsare required to describe 50% of the variance.When the amplitude of a particular eigenvectorattains a large value during a month or season,the observed anomaly field closely resembles thecorresponding eigenvector. 2) The first eigenvector computed from normalized values of each variable corresponds to a general excess or deficit of temperature, precipitationor pressure (mass) over nearly the entire UnitedStates. The second and third eigenvectors of eachvariable represent 'general gradients in the eastwest and north-south directions, respectively. 3) The amplitudes of the eigenvectors of differentvariables are correlated. These cross-correlationsare consistent with physical expectations and, .insome cases, show a strong seasonal dependence. 4) The month-to-month persistence of the anomalypatterns is also seasonally dependent. The firstmode of temperature and of pressure shows thestrongest persistence in summer; however, thehighest persistences are those of the third temperature eigenvector during fall and winter. The monthlypersistence of the precipitation fields is very small. 5) Persistence on the seasonal time scale is generally largest for temperature 'and largest whensummer is the antecedent season. The seasonalpersistences of the amplitudes of the temperatureeigenvectors are generally consistent with the patterns of the persistence of station temperature(Namias, 1978).0.60.40.20.6 D.6 co 10 4 2 1.5 1.0 0.75 0.50 ~ PERIOD, yearsFIG. 13. As in Fig. 12 except for the coefficients of the - precipitation eigenvectors.MAY 1980 JOHN E. WALSH AND ANTHONY MOSTEK 629 -'~[_1 I I I I I s~ _ 0.40.2 -- ' . _95%_L, E~~ 0 (I.2 0.6 $3 - 0.2 m 10 4 2 1.S 1.0 0.75 0.50 ~[RIOD, yearsF~G. 14. As in Fig. 12 except for the coefficients of the sea level pressure eigenvectors. 6) The most prominent feature of the computedfrequency spectra is the peak at 2.1 years in the'amplitude of the third temperature eigenvector.While peaks in the other computed spectra aresignificant at the 95% level, some of these arelikely due to chance. The modest values of the monthly and seasonalpersistences obtained here imply that their value inforecasting applications will at best be limited. However, the scales of the anomaly patterns suggestthat the eigenvector representation of the meteorological data may be useful in delinbating relationships between atmospheric anomalies and seasurface temperature, snow cover, or other surfacefluctuations. Namias (e.g., 1964; 1974) has suggested a number of such associations, while; Harnackand Landsberg (1978) have computed the laggedcorrelations between the amplitudes of oceantemperature eigenvectors and temperatures overspecified regions of the United States. S~ach studies may be aided by the consideration of atmospheric anomaly patterns. Walsh and Johnson(1979), for example, found that correlations between spatial patterns of high-latitude temperatureand sea ice extent were considerably higher thanthe correlations between area-averaged values'of thesame quantities. Further applications of the eigenvector approach are possible in the statisticalmodeling and forecasting of crop yields, since cropyield anomalies often show considerable spatialcoherence. Our final comment, which pertains to studies ofthe forcing of the atmosphere by external variables(e.g., SST fields, snow cover), is that the orthogonality of the type of empirical functions used here maybe an undesirable constraint in some cases. Specifically, all eigenvectors other than the first are constrained, to be orthogonal to all previously constructedeigenvectors of the set. It is very possible that anatmospheric response to an SST anomaly, for exampie, may be "smeared" over several atmosphericeigenvectors rather than isolated in a single eigenvector. A canonical correlation analysis may bemore appropriate in such studies. Acknowledgments. This work was supported bythe National Science Foundation, Climate DynamicsProgram, through Grant ATM77-22510. Computingfacility support was provided by the National Centerfor Atmospheric Research and by the Universityof Illinois Research Board. We wish to thankD, McNeely for typing the manuscript, J. 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